Gaussian Process Regression for Maximum Entropy Distribution
- Resource Type
- Working Paper
- Authors
- Sadr, Mohsen; Torrilhon, Manuel; Gorji, M. Hossein
- Source
- Journal of Computational Physics, Volume 418, 2020, 109644
- Subject
- Statistics - Machine Learning
Computer Science - Machine Learning
Mathematical Physics
Physics - Data Analysis, Statistics and Probability
- Language
Maximum-Entropy Distributions offer an attractive family of probability densities suitable for moment closure problems. Yet finding the Lagrange multipliers which parametrize these distributions, turns out to be a computational bottleneck for practical closure settings. Motivated by recent success of Gaussian processes, we investigate the suitability of Gaussian priors to approximate the Lagrange multipliers as a map of a given set of moments. Examining various kernel functions, the hyperparameters are optimized by maximizing the log-likelihood. The performance of the devised data-driven Maximum-Entropy closure is studied for couple of test cases including relaxation of non-equilibrium distributions governed by Bhatnagar-Gross-Krook and Boltzmann kinetic equations.